"Why is the sky blue?"
It's one of those questions that most people don't know the answer to, while others know at least the basic explanation that the atmosphere scatters blue light more strongly than the other visible wavelengths. Ask why that happens and you'll enter the realm of some interesting and somewhat complicated physics. We'll do that later, and do an easier one today.
Kids sometimes also ask why water is blue. The most common answer is that it isn't - the blue of the ocean is attributed to reflected sky or something similar, while the water itself is clear. There's some truth to that, but it's not the whole story. Water really is blue - a very very faint almost transparent blue.
Let's take a look at Wikipedia's plot of the absorption spectrum of water:
It's a logarithmic plot, so for instance water absorbs more than a billion times more ultraviolet than it does at the bottom of its transmission window. It's no coincidence that visible light happens to be transmitted the best. There would be very little point in having eyes that can see wavelengths that don't make from the sun through the atmospheric water vapor in any reasonable quantity.
But you may notice that although visible light is transmitted very well, blue wavelengths are transmitted better than red ones. After passing through a few dozen meters the difference is enough to be noticeable; much more of the blue light has passed through without being absorbed.
The qualitative reason for the gap is straightforward. The bending and stretching of the bonds between the hydrogen and oxygen typically have energies in the infrared and microwave frequencies, while the electronic energy levels typically have energies in the ultraviolet and higher. In the middle water just doesn't have much internal structure with resonances near those frequencies and so most energy with those frequencies passes straight through.
And that's why water is blue.
Water absorbance edging into the deep red arises from combination and overtone bands, not from pure vibronic transitions.
There would be very little point in having eyes that can see wavelengths that don't make from the sun through your water-filled eyeballs to your retina. In the bad old days cataract extractions left the patient able to see down to about 350 nm. Blacklight was visible and retinas fried.
Today the opacified natural lens is replaced with a Plexiglas IOL implant. It corrects vision to 20/20 at one distance. It contains a hydroxyphenylbenzotriazole UV-absorber down to 400 nm colorless or ~415 nm pale yellow (e.g., Tinuvin 326) for extra retina protection. Variable focus IOLs are not quite spiffy yet.
Nice complementary post here which goes into specific molecular vibrations a bit.
A related question. Having lived long enough to have gray hair I was faced with the question (from my wife) "Why is your hair black (or at least dark) when its wet?" Hated not having a good answer to that. Its clearly not differential absorption because the distance light has to travel is much less than an e-folding.
When my kid asks why the sky is blue, I'm busting out Jackson.
I'm interested in your explanation for the sky being blue. You made it sound like you might go into technical details.
Bonus points if you include loop diagrams beyond the one loop level if you are using QED. :)
Scuba divers know that reds disappear pretty quickly at depth. I actually once bought a wetsuit with red trim, thinking that it would be easy for my buddy to pick out in a crowd of divers. Oooooppps!
I read that backreaction post before too (like Patrick #2 said).
I particularly like this tidbit: the vibration frequency of the bonds goes down if you use deuterium in your water instead of hydrogen, and you get colourless water.
If you define the atmosphere's color in terms of its tranmission spectrum, the same way you did for water, it is actually red. That the atmosphere is a red filter can be seen during lunar eclipses.
The =current= answer to "Why is the Sky Blue?" can be found in Gotz Hoeppe's wonderful book "Why the Sky is Blue; Discovering the Color of Life" translated from the German. It is NOT a trivial question and even the most sophisticated single physics answers that people give are actually only partially true. There is more than one thing going on at a time in the sky.
This is good too, if you'd like a physics textbook that has a lengthy discussion of why the sky is blue:
"Fundamentals of Atmospheric Radiation" by Craig F. Bohren and Eugene Clothiaux
Heavy water isn't...